Event beta: realized loading of asset returns on event-probability news

Regresses asset returns on the innovations of a traded event probability, $$r_t = \alpha + b\, \Delta q_t + \gamma' c_t + u_t,$$ with Newey-West (Bartlett/HAC) standard errors. To first order the model implies $r_t \approx \Delta\eta\,\Delta q_t$, so the slope b is the returns-based estimate of the event exposure $\widehat{\Delta\eta}$.

Usage

event_beta(asset, x, deta = NULL, controls = NULL, lags = NULL)

# S3 method for class 'event_beta'
print(x, ...)

Arguments

asset: A data.frame with a time column and either a return column (ret) or a price column (adjusted, close, or price; log returns are computed).
x: An event_prices object (or coercible); its probability innovations $\Delta q_t$ are the regressor. Observations are matched on the calendar date.
deta: Optional externally measured event exposure $\Delta\eta$; enables the $\beta = 1$ test.
controls: Optional data.frame with a time column and control variables (e.g. market returns), matched on date.
lags: Newey-West lag order; default $\lfloor 4 (n/100)^{2/9} \rfloor$. Use lags = 0 for heteroskedasticity-robust (HC0) errors.
...: Unused (for the print method).

Value

An object of class event_beta: a list with

coefficients: tibble of terms, estimates, HAC standard errors, t-statistics, and p-values.
deta_hat, deta_se: the slope on $\Delta q$ and its SE.
eta1, eta2: model-implied levels (see Details).
beta, beta_se, beta_z, beta_p: (only with deta) the loading $b/\Delta\eta$ and the Wald test of $\beta = 1$.
r2, n, lags: regression diagnostics; r2 is the realized variance share of event news over the sample.

Details

What is (and is not) identified. Returns identify only the spread $\Delta\eta = \eta_1 - \eta_2$, not the outcome-conditional levels $\eta_1, \eta_2$ separately (those require event-spanning option smiles). Consequently the loading test $\beta = 1$ is only meaningful against an externally measured exposure: supply deta (e.g. option-implied, or from an independent sample) and the function reports $\beta = b / \Delta\eta$ with a Wald test of $\beta = 1$. Without deta, the regression is exactly identified and only $\widehat{\Delta\eta}$ is reported.

Under the risk-neutral adding-up constraint $q\,\eta_1 + (1-q)\,\eta_2 = 1$, point estimates of the levels can be backed out as $\eta_1 = 1 + (1-q)\Delta\eta$ and $\eta_2 = 1 - q\Delta\eta$; these are model-implied, not independently identified, and are returned for convenience (evaluated at the sample-average q).

Methods (by generic)

print(event_beta): Print method.

Examples

data(djt2024)
data(polymarket2024)
ep <- pm_daily(as_event_prices(polymarket2024))
event_beta(djt2024, ep)
#> -- Event-beta regression (Newey-West, 4 lags)
#> Event exposure deta_hat = 1.2765 (se 0.4838, t = 2.64), n = 108, R^2 = 0.064
#> Model-implied levels at mean q = 0.554: eta1 = 1.5699, eta2 = 0.2934
#> (No external deta supplied: levels/loading test not identified from returns alone.)